Will not start when hot. starter makes no different types of noise.

You have the polarity of the battery backward somewhere. Did you replace the starter and hook it up backwards. Difficult but possible. Check your positive and negative on the battery itself.

Without being able to hear the sound it's hard to point you in the right direction without more details. My first assumption from what you've described would be that the noise is present only while cranking/initial starting. If this is so, there are a few possible reasons for this. 1. The starter that was put is is faulty. 2. The starter was incorrectly installed. (Some starters actually have an alignment and/or shims although it's uncommon on most cars.) 3. The starter that was installed was the incorrect starter for your vehicle. (A lot of vehicles have different starters for automatic and manual transmissions that'll look identical and bolt on but the throw of the starter gear is different and/or the gear's teeth on the starter is different and doesn't properly mesh with the ring gear. This will ruin the teeth on the ring gear on your flex plate/flywheel.) 4. The teeth on the ring gear of your flex plate/flywheel were previously worn because of your old starter and now the teeh on the starter gear are not properly meshing. (This will ruin any starter that you put in.)

Hope this helps. If you can provide any more information, I'd be happy to help you to further narrow down the problem. e.g. Year, make, model, engine size, transmission type of the vehicle and part number of the starter installed. A better description of the noise and conditions of occurrence. e.g. A rough grinding noise while holding the key in the start position followed by a hollow metallic pinging noise or prolonged whining. Etc.

What is litre size of engine, automatic tranny or manual? Check the wiring circuits at the starter for voltage,use a test light, One circuit is hot all the time, the other circuit goes hot when starter relay is energized. Any testing at the starter make sure tranny is in park or neutral and the parking brake is set. The clicking noise may be the starter relay.

you need shims on the start. some of the older gm cars need shims when a new starter is installed

CHECK FOR LOOSE OR MISSING STARTER BOLTS OR STARTER FAULTY.

are you making sure you are receiving the correct starter ?? different ones for manual and automatic transmissions.

dose the starter motor make any noises? some time starters fail to work when they are hot it may be worth having the stater checked

Starter has teeth that mesh with teeth on the flex plate . most of these type grinding noises are do to missing teeth on the starter gear or flex plate missing teeth .Does your vehicle have a automatic transmission ? Have you had starter replaced lately ?

defective starter

shack

Check your battery cable connections and check for corrosion. Make sure you have a good, clean ground.